While the dictionary at geology.com does not appear to carry fluvial, the dictionary of geography at itseducation.asia gives the following definition:
lit. of a river. Used to distinguish processes and landforms from similar ones that may be produced by a different agent, e.g. fluvial deposition rather than glacial deposition.
Merriam-Webster defines fluvial as follows:
1 of, relating to, or living in a stream or river
2 produced by the action of a stream
a fluvial plain
Oxford Living Dictionaries gives the following definition:
Of or found in a river.
Middle English: from Latin fluvialis, from fluvius ‘river’, from fluere ‘to flow’.
In particular, note the etymology given.
The Online Dictionary of Etymology agrees:
"pertaining to a river,"
late 14c., from Latin fluvialis "of a river," from fluvius "a river, stream, running water," related to fluere "to flow" (see fluent).
As far as I can see, you can look through all the definitions Onelook finds for fluvial and none of them give any suggestion that fluvial can be used in any context other than in reference to rivers. Ponds and streams is as far a stretch from a river as any goes, in the 1913 Webster. (A rather pedantic argument could be made that as fluvial derives from a word referring to flowing water it is applicable even to a broken drain, but I can't find any evidence for current usage to lend credence to this kind of speculation.)
Moreover, the sense the geographical dictionary entry above gives would suggest that flooding from a pipe would be specifically excluded from the meaning of fluvial, and that it would be misleading to use the word in such a context.
Based on all this, I would say that the answer to your question
Could I use "fluvial" to describe water originating from a man-made source[?]
is no, not in the case at hand, despite what you were taught.
(However, I would see no problem using it in relation to deposits from, say, a diverted river, which is arguably a man-made source, albeit one that is still a river.)
To go on, your example sentence works perfectly well without fluvial and is completely clear without anything taking its place:
There was a significant deposit left on the road from the flooding caused by the burst pipe.